Using Math to Fight Cancer

Remember when you wondered if you’d ever use calculus in real life? Researchers at the University of Miami (UM) and the University of Heidelberg in Germany have used math modeling to predict tumor growth and how cancer metastasizes in humans.

In other words, they used mathematics to create a model that can predict how a tumor will grow, and if and how it will metastasize. Their results were published in Nature’s new online journal Scientific Reports.

Math models are not unusual in medical settings. In fact, they’ve been used in a variety of cancer studies. But the UM and University of Heidelberg model is different from others—and that translates to more accurate predictions for individual patients.

First, previous models did not consider how the tumor and the network of blood vessels, called the vasculature, coexist. These blood vessels act as a food source for the tumor, and in turn are affected by the tumor itself.

“This feedback between the tumor and vasculature is missing from nearly all existing cancer models because it is difficult to treat both at the same time,” says Neil Johnson, PhD, professor of physics, director of the Complexity Research Group at UM College of Arts and Sciences, and co-principal investigator of the study.

“And yet this feedback is exactly what characterizes the complexity of the real tumors that patients have.”

The new model also addresses the individual cells within the tumor differently. (Like all parts of the body, tumors are made up of millions of tiny cells. In fact, these cancer cells—replicating over and over—are how the tumor grows.)

Previous models looked at each cell—which is a huge and potentially impossible feat—or looked at the cells as a large, consistent mass. The new model creates a kind of patchwork quilt of areas of the tumor to examine. When all of these pieces are considered as a whole, doctors can get a more accurate idea of how the tumor will grow.

Finally, researchers put the model to work to predict how or if the tumor will spread or metastasize.

“Until now, the problem of primary tumor growth and metastasis have been treated as separate problems,” Johnson says.

What does all of this mean for patients and doctors? The potential applications for the model are impressive: “Eventually, we believe that a fully refined version of this model could run on a doctor’s hand-held PDA,” Johnson says.

This means that in the future, cancer doctors may have—in the palm of their hands—the ability to offer diagnoses based on the characteristics of individual tumors. That could translate to tailor-made treatments that suit the aggressiveness of individual tumors, rather than doctors’ best guesses based on how similar tumors have progressed in other patients.

Connect the Dots

Read the study and view graphs of the model at Scientific Reports. For more information about cancer, visit the National Institute of Health’s MedlinePlus. The Society for Industrial and Applied Mathematics (SIAM) offers a good explanation of how math models are used in medical research.